G给出一个由循环链表表示的两个多项式，任务是通过将同一变量的幂的系数相加来将这两个多项式相加。
注意：在给定的多项式中，包含x的较高幂的项将首先出现。
例子：
Input:
1st Number = 5x^2 * y^1 + 4x^1 * y^2 + 3x^1 * y^1 + 2x^1
2nd Number = 3x^1 * y^2 + 4x^1
Output:
5x^2 * y^1 + 7x^1 * y^2 + 3x^1 * y^1 + 6x^1
Explanation:
The coefficient of x^2 * y^1 in 1st numbers is 5 and 0 in the 2nd number. Therefore, sum of the coffiecient of x^2 * Y^1 is 5.
The coefficient of x^1 * y^2 in 1st numbers is 4 and 3 in the 2nd number. Therefore, sum of the coefficient of x^1 * Y^2 is 7.
The coefficient of x^1 * y^1 in 1st numbers is 3 and 0 in the 2nd number. Therefore, sum of the coefficient of x^1 * Y^1 is 2.
The coefficient of x^1 * Y^0 in 1st numbers is 2 and 4 in the 2nd number. Therefore, sum of the coefficient of x^1 * Y^0 is 6.
Input:
1st Number = 3x^3 * y^2 + 2x^2 + 5x^1 * y^1 + 9y^1 + 2
2nd Number = 4x^3 * y^3 + 2x^3 * y^2 + 1y^2 + 3
Output:
4x^3 * y^3 + 5x^3 * y^2 + 2x^2 + 5x^1 * y^1 + 1y^2 + 9y^1 + 5
方法：按照以下步骤解决问题：
- 创建两个循环链接列表，其中每个节点将由系数， x的幂， y的幂以及指向下一个节点的指针组成。
- 遍历两个多项式并检查以下条件：
- 如果第一多项式的x的功率比的多项式1生成的多项式和增加计数器第一多项式的第二多项式然后存储节点的x的功率。
- 如果第一个多项式的x的幂小于第二个多项式的x幂，则将第二个多项式的节点存储在结果多项式中，并增加多项式2的计数。
- 如果第一多项式的x的功率等于第一多项式的Y的第二多项式和的功率x的功率大于第二多项式的Y的功率然后第一多项式的节点存储在的多项式1生成的多项式和增加计数器值。
- 如果第一多项式的x的幂等于第二多项式的x的幂且第一多项式的y的幂等于第二个多项式的y的幂，则将两个多项式的系数之和存储在所得多项式中，并增加两个多项式的计数1和多项式2 。
- 如果在第一个多项式或第二个多项式中还有要遍历的节点，则将它们附加到结果多项式中。
- 最后，打印结果多项式。
下面是上述方法的实现：
C++
// C++ program to implement
// the above approach
#include
using namespace std;
// Structure of a node
// in a circular linked list
struct Node {
// Stores coefficient
// of a node
int coeff;
// Stores power of'
// variable x of a node
int powx;
// Stores power of
// variable y of a node
int powy;
// Stores pointer
// to next node
struct Node* next;
};
// Function to dynamically create a node
void create_node(int c, int p1, int p2,
struct Node** temp)
{
// Stores new node
struct Node *r;
// Stores temp node
struct Node *z
= *temp;
// Dyanamically create a new node
r = (struct Node*)malloc(
sizeof(struct Node));
// Update coefficient
// of r
r->coeff = c;
// Update power of
// variable x in r
r->powx = p1;
// Update power of
// variable y in r
r->powy = p2;
// If z is null
if (z == NULL) {
// Update temp node
(*temp) = r;
// Update next pointer
// of temp node
(*temp)->next = (*temp);
}
else {
// Update next pointer
// of z
r->next = z->next;
// Update next pointer
// of z
z->next = r;
// Update temp Node
(*temp) = r;
}
}
// Function to add polynomial of two list
void add_poly(struct Node* poly1,
struct Node* poly2, struct Node** temp)
{
// Stores head node of polynomial1
struct Node *start1 = poly1;
// Stores head node of polynomial1
struct Node *start2 = poly2;
// Update poly1
poly1 = poly1->next;
// Update poly2
poly2 = poly2->next;
// Traverse both circular linked list
while ((poly1 != start1 &&
poly2 != start2)) {
// Stores new node
struct Node* r;
// Stores temp node
struct Node* z
= *temp;
// Dynamically create a new node
r = (struct Node*)malloc(
sizeof(struct Node));
// Update coefficient of r
r->coeff = 0;
// If power of x of poly1 is
// greater than power of x of poly2
if (poly1->powx > poly2->powx) {
// Update coefficient of r
r->coeff = poly1->coeff;
// Update of power of x in r
r->powx = poly1->powx;
// Update of power of y in r
r->powy = poly1->powy;
// Update poly1
poly1 = poly1->next;
}
// If power of x of 1st polynomial is
// less than power of x of 2nd poly
else if (poly1->powx < poly2->powx) {
// Update coefficient OF r
r->coeff = poly2->coeff;
// Update power of x in r
r->powx = poly2->powx;
// Update power of y in r
r->powy = poly2->powy;
// Update ploy2
poly2 = poly2->next;
}
// If power of x of 1st polynomial is
// equal to power of x of 2nd poly
else {
// Power of y of 1st polynomial is
// greater than power of y of poly2
if (poly1->powy > poly2->powy) {
// Update coefficient of r
r->coeff = poly1->coeff;
// Update power of x in r
r->powx = poly1->powx;
// Update power of y in r
r->powy = poly1->powy;
// Update poly1
poly1 = poly1->next;
}
// If power of y of poly1 is
// less than power of y of ploy2
else if (poly1->powy <
poly2->powy) {
// Update coefficient of r
r->coeff = poly2->coeff;
// Update power of x in r
r->powx = poly2->powx;
// Update power of y in r
r->powy = poly2->powy;
// Update poly2
poly2 = poly2->next;
}
// If power of y of 1st poly is
// equal to power of y of ploy2
else {
// Update coefficient of r
r->coeff = poly2->coeff
+ poly1->coeff;
// Update power of x in r
r->powx = poly1->powx;
// Update power of y in r
r->powy = poly1->powy;
// Update poly1
poly1 = poly1->next;
// Update poly2
poly2 = poly2->next;
}
}
// If z is null
if (z == NULL) {
// Update temp
(*temp) = r;
// Update next pointer
// of temp
(*temp)->next = (*temp);
}
else {
// Update next pointer
// of r
r->next = z->next;
// Update next pointer
// of z
z->next = r;
// Update temp
(*temp) = r;
}
}
// If there are nodes left to be
// traversed in poly1 or poly2 then
// append them in resultant polynomial .
while (poly1 != start1 ||
poly2 != start2) {
// If poly1 is not empty
if (poly1 != start1) {
// Stores new node
struct Node *r;
// Stores temp node
struct Node *z = *temp;
// Create new node
r = (struct Node*)malloc(
sizeof(struct Node));
// Update coefficient or r
r->coeff = poly1->coeff;
// Update power of x in r
r->powx = poly1->powx;
// Update power of y in r
r->powy = poly1->powy;
// Update poly1
poly1 = poly1->next;
// If z is null
if (z == NULL) {
// Update temp
(*temp) = r;
// Update pointer
// to next node
(*temp)->next = (*temp);
}
else {
// Update next pointer
// of r
r->next = z->next;
// Update next pointer of z
z->next = r;
// Update temp
(*temp) = r;
}
}
// If poly2 is not empty
if (poly2 != start2) {
// Stores new node
struct Node *r;
// Stores temp node
struct Node *z = *temp;
// Create new node
r = (struct Node*)malloc(
sizeof(struct Node));
// Update coefficient of z
z->coeff = poly2->coeff;
// Update power of x in z
z->powx = poly2->powx;
// Update power of y in z
z->powy = poly2->powy;
// Update poly2
poly2 = poly2->next;
// If z is null
if (z == NULL) {
// Update temp
(*temp) = r;
// Update next pointer
// of temp
(*temp)->next = (*temp);
}
else {
// Update next pointer
// of r
r->next = z->next;
// Update next pointer
// of z
z->next = r;
// Update temp
(*temp) = r;
}
}
}
// Stores new node
struct Node *r;
// Stores temp node
struct Node *z = *temp;
// Create new node
r = (struct Node*)malloc(
sizeof(struct Node));
// Update coefficient of r
r->coeff = 0;
// If power of x of start1 greater than
// power of x of start2
if (start1->powx > start2->powx) {
// Update coefficient of r
r->coeff = start1->coeff;
// Update power of x in r
r->powx = start1->powx;
// Update power of y in r
r->powy = start1->powy;
}
// If power of x of start1 less than
// power of x of start2
else if (start1->powx < start2->powx) {
// Update coefficient of r
r->coeff = start2->coeff;
// Update power of x in r
r->powx = start2->powx;
// Update power of y in r
r->powy = start2->powy;
}
// If power of x of start1 equal to
// power of x of start2
else {
// If power of y of start1 greater than
// power of y of start2
if (start1->powy > start2->powy) {
// Update coefficient of r
r->coeff = start1->coeff;
// Update power of x in r
r->powx = start1->powx;
// Update power of y in r
r->powy = start1->powy;
}
// If power of y of start1 less than
// power of y of start2
else if (start1->powy <
start2->powy) {
// Update coefficient of r
r->coeff = start2->coeff;
// Update power of x in r
r->powx = start2->powx;
// Update power of y in r
r->powy = poly2->powy;
}
// If power of y of start1 equal to
// power of y of start2
else {
// Update coefficient of r
r->coeff = start2->coeff
+ start1->coeff;
// Update power of x in r
r->powx = start1->powx;
// Update power of y in r
r->powy = start1->powy;
}
}
// If z is null
if (z == NULL) {
// Update temp
(*temp) = r;
// Update next pointer
// of temp
(*temp)->next = (*temp);
}
else {
// Update next pointer of r
r->next = z->next;
// Update next pointer of z
z->next = r;
// Update temp
(*temp) = r;
}
}
// Display the circular linked list
void display(struct Node* node)
{
// Stores head node of list
struct Node* start = node;
// Update node
node = node->next;
// Traverse the list
while (node != start &&
node->coeff != 0) {
// Print coefficient of
// current node
cout << node->coeff;
// If power of variable x
// is not zero
if (node->powx != 0)
cout << "x^" << node->powx;
// If power of variable x
// and y is not zero
if(node->powx != 0 &&
node->powy != 0)
cout<<" * ";
// If power of variable y
// is not zero
if (node->powy != 0)
cout << "y^" << node->powy;
// Add next term of
// the polynomial
if (node != start &&
node->next->coeff != 0) {
cout << " + ";
}
// Update node
node = node->next;
}
// Print coefficient of
// current node
cout << node->coeff;
// If power of variable x
// is not zero
if (node->powx != 0)
cout << "x^" << node->powx;
// If power of variable y
// is not zero
if (node->powy != 0)
cout << "y^" << node->powy;
cout << "\n\n";
}
// Driver Code
int main()
{
// Stores node of
// first polynomial
struct Node *poly1 = NULL;
// Stores node of
// second polynomial
struct Node *poly2 = NULL;
// Stores node of resultant
// polynomial
struct Node *store = NULL;
// Create first polynomial
create_node(5, 2, 1, &poly1);
create_node(4, 1, 2, &poly1);
create_node(3, 1, 1, &poly1);
create_node(2, 1, 0, &poly1);
create_node(3, 0, 1, &poly1);
create_node(2, 0, 0, &poly1);
// Create second polynomial
create_node(3, 1, 2, &poly2);
create_node(4, 1, 0, &poly2);
create_node(2, 0, 1, &poly2);
create_node(6, 0, 0, &poly2);
// Function call to add
// two polynomial
add_poly(poly1, poly2, &store);
// Display polynomial 1
cout << "Polynomial 1"
<< "\n";
display(poly1);
// Display polynomial 2
cout << "Polynomail 2"
<< "\n";
display(poly2);
// Display final addition of 2-variable polynomial
cout << "Polynomial after addition"
<< "\n";
display(store);
return 0;
} 输出：
Polynomial 1
5x^2 * y^1 + 4x^1 * y^2 + 3x^1 * y^1 + 2x^1 + 3y^1 + 2
Polynomail 2
3x^1 * y^2 + 4x^1 + 2y^1 + 6
Polynomial after addition
5x^2 * y^1 + 7x^1 * y^2 + 3x^1 * y^1 + 6x^1 + 5y^1 + 8
时间复杂度： O(M + N)，其中M和N分别是第一列表和第二列表中的节点数。
辅助空间： O(M + N)